Problem: Simplify the following expression: $ q = \dfrac{t + 10}{t - 1} - \dfrac{-9}{4} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{t + 10}{t - 1} \times \dfrac{4}{4} = \dfrac{4t + 40}{4t - 4} $ Multiply the second expression by $\dfrac{t - 1}{t - 1}$ $ \dfrac{-9}{4} \times \dfrac{t - 1}{t - 1} = \dfrac{-9t + 9}{4t - 4} $ Therefore $ q = \dfrac{4t + 40}{4t - 4} - \dfrac{-9t + 9}{4t - 4} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{4t + 40 - (-9t + 9) }{4t - 4} $ Distribute the negative sign: $q = \dfrac{4t + 40 + 9t - 9}{4t - 4}$ $q = \dfrac{13t + 31}{4t - 4}$